A223611 Numbers k whose abundance is 20: sigma(k) - 2*k = 20.

176, 1376, 3230, 3770, 6848, 114256, 125696, 544310, 561824, 740870, 2075648, 4199030, 4607296, 8436950, 33468416, 134045696, 199272950, 624032630, 1113445430, 1550860550, 85905593344, 2199001235456, 35184284008448, 10805836895078390, 103285638050111990

Offset: 1

Author

Donovan Johnson, Mar 23 2013

Keywords

• nonn

Comments

Suggested by N. J. A. Sloane and Robert G. Wilson v.

a(22) > 10^12.

a(23) > 10^13. - Giovanni Resta, Mar 29 2013

a(29) > 10^18. - Hiroaki Yamanouchi, Aug 23 2018

Any term x of this sequence can be combined with any term y of A223607 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. - Timothy L. Tiffin, Sep 13 2016

Every number of the form 2^(j-1)*(2^j - 21), where 2^j - 21 is prime, is a term. - Jon E. Schoenfield, Jun 02 2019

Examples

			For k = 544310, sigma(k) - 2*k = 20.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..28

Crossrefs

Cf. A000203, A033880, A223607 (deficiency 20).

Programs

Magma

[n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq 20]; // Vincenzo Librandi, Sep 14 2016

Mathematica

Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == 20 &] (* Vincenzo Librandi, Sep 14 2016 *)

PARI

for(n=1, 10^8, if(sigma(n)-2*n==20, print1(n ", ")))

Extensions

a(22) from Giovanni Resta, Mar 29 2013

a(23)-a(25) from Hiroaki Yamanouchi, Aug 23 2018